Compare Unit Fractions

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Videos, examples, solutions, and lessons to help Grade 3 students learn how to compare unit fractions by reasoning about their size using fraction strips.

Common Core Standards: 3.NF.3d, 3.NF.1, 3.NF.3a, 3.NF.3b, 3.NF.3c, 3.G.2

New York State Common Core Math Grade 3, Module 5, Lesson 10
Worksheets for Grade 3

Application Problem

Sarah makes soup. She divides each batch equally into thirds to give away. Each family that she makes soup for gets 1 third of a batch. Sarah needs to make enough soup for 5 families. How much soup does Sarah give away? Write your answer in terms of batches.

Bonus: What fraction will be left over for Sarah?

Lesson 10 Concept Development

Using Fraction Strips

  1. Fold fraction strips into halves, thirds,fourths, sixths, and eighths.
  2. Arrange the strips in order from the largest to the smallest unit. Notice that eighths are the smallest even though the number ‘8’ is the biggest. When the whole is folded into more units, then each unit is smaller. I only folded 1 time to get halves, and they’re the biggest.
  3. Look at 1 half and 1 third. Which unit is larger? 1 half
    Explain how you know.
    I can just see 1 half is bigger on the strip.
    When we split it between 2 people, the pieces are bigger than if we split it between 3 people. There are fewer pieces, so the pieces are bigger.

Using Circles

  1. Draw 5 circles that are the same size to represent pizzas
  2. Partition the circle into halves, thirds,fourths, sixths, and eighths. Label the unit fraction.
  3. What’s happening to our pieces the more we cut? Compare your drawings to your fraction strips. Do you notice the same pattern as with your fraction.

Lesson 10 Homework

  1. Each fraction strip is 1 whole. All the fraction strips are equal in length. Color one fractional unit in each strip. Then answer the questions below.
  2. Circle less than or greater than. Whisper the complete sentence.
    a. 1/2 is ___ 1/3
    b. 1/9 is ___ 1/2
    c. 1/4 is ___ 1/2
    d. 1/4 is ___ 1/9
    e. 1/5 is ___ 1/3
    f. 1/5 is ___ 1/4
    g. 1/2 is ___ 1/5
    h. 6 fifths is ___ 3 thirds
  3. After his football game, Malik drinks 1/2 liter of water and 1/3 liter of juice. Did Malik drink more water or juice? Draw and estimate to partition. Explain your answer.
  4. Compare unit fractions and write <, >, or =.
    a. 1 fourth ___ 1 eighth
    b. 1 seventh ___ 1 fifth
    c. 1 eighth ___ 1/8
    d. 1 twelfth ___ 1/10
    e. 1/15 ___ 1 thirteenth
    f. 3 thirds ___ 1 whole
  5. Write a word problem using comparing fractions for your friends to solve. Be sure to show the solution so that your friends can check their work.

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